This paper is part of a larger project in which we systematically study the chemical abundances of extra-galactic post-asymptotic giant branch (post-AGB) stars. The aim of our programme is to derive chemical abundances of stars covering a large range in luminosity and metallicity with the ultimate goal of testing, constraining, and improving our knowledge of the poorly understood AGB phase, especially the third dredge-up mixing processes and associated s-process nucleosynthesis. Post-AGB photospheres are dominated by atomic lines and indicate the effects of internal chemical enrichment processes over the entire stellar lifetime. In this paper, we study two carefully selected post-AGB stars: J051213.81-693537.1 and J051848.86-700246.9 in the Large Magellanic Cloud (LMC). Both objects show signs of s-process enhancement. The combination of favourable atmospheric parameters for detailed abundance studies and their known distances (and hence luminosities and initial masses) make these objects ideal probes of the AGB third dredge-up and s-process nucleosynthesis in that they provide observational constraints for theoretical AGB models.